Henri & Renaud Lifchitz's PRP Top records

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

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1-250	251-500	501-750	751-1000	1001-1250	1251-1500	1501-1750	1751-2000
2001-2250	2251-2500	2501-2750	2751-3000	3001-3250	3251-3500	3501-3750	3751-4000
4001-4250	4251-4500	4501-4750	4751-5000	5001-5250	5251-5500	5501-5750	5751-6000
6001-6250	6251-6500	6501-6750	6751-7000	7001-7250	7251-7500	7501-7750	7751-8000
8001-8250	8251-8500	8501-8750	8751-9000	9001-9250	9251-9500	9501-9750	9751-10000

Rank	Probable prime	Digits (> 50000)	Who ?	When ?
9001	(31*2^341006-1)/3	102655	Lelio R Paula	03/2014
9003	2^341004-173	102653	Lelio R Paula	08/2011
9002	20^78901+3	102653	Lelio R Paula	10/2016
9004	(2^341001+1674)/2	102652	Stefano Morozzi	09/2020
9005	5^146853-52	102646	Lelio R Paula	10/2016
9006	2^340969-216931	102642	Enzo Doria	05/2014
9007	122^49196+121	102641	Norbert Schneider	10/2018
9008	2^340952+1870021	102637	Enzo Doria	05/2016
9009	5*2^340940-3	102634	Lelio R Paula	08/2014
9010	(6^131891+1)/7	102631	Paul Bourdelais	01/2010
9011	(11*10^102629-23)/3	102630	Robert Price	09/2021
9012	3^215094+5*2^215094	102626	Jon Grantham	08/2023
9013	25876^9239+9239^25876	102615	Hans Havermann	02/2019
9014	(4*10^102612+83)/3	102613	Robert Price	02/2018
9015	(234^43313-1)/20184091	102611	Aurel Gibier	03/2025
9017	75^54717+74	102598	Norbert Schneider	01/2015
9016	(17*10^102597+13)/3	102598	Robert Price	01/2019
9018	2^340806-20393	102593	Enzo Doria	06/2013
9019	(2^340790+5)/138267	102583	Lelio R Paula	12/2013
9020	6^131821+77	102577	Lelio R Paula	10/2016
9021	(203*10^102561-11)/3	102563	Robert Price	12/2020
9022	(67^56171-1)/2053280351166	102561	Paul Vanderveen	05/2025
9023	2^340688-29	102558	Henri Lifchitz	05/2005
9024	2^340685-109101	102557	Enzo Doria	04/2014
9025	65^56567-64	102552	Norbert Schneider	11/2014
9026	26230^8121+8121^26230	102550	Hans Havermann	03/2019
9027	(64*10^102547+161)/9	102548	Robert Price	08/2022
9028	(8*10^102541+49)/3	102542	Robert Price	05/2020
9029	(536*10^102533-23)/9	102535	Robert Price	02/2020
9030	2^340547-108897	102515	Enzo Doria	03/2014
9031	(2^340536+778)/2	102512	Stefano Morozzi	09/2020
9032	25592^10119+10119^25592	102500	Hans Havermann	02/2019
9033	(5*10^102492-23)/9	102492	Serge Batalov	11/2022
9034	7^121268+82	102484	Lelio R Paula	10/2016
9035	(6883*2^340443-1)/162401	102483	Lelio R Paula	05/2015
9036	2^340434-5955	102481	Lelio R Paula	11/2016
9037	(7*10^102480-19)/3	102481	Robert Price	10/2020
9038	(2^340381+47)/7	102465	Lelio R Paula	12/2013
9039	111^50095+110	102461	Norbert Schneider	04/2017
9040	180^45427-45427^180	102451	Norman Luhn	09/2024
9041	2^340291-20301	102438	Enzo Doria	06/2013
9042	12^94915+89	102431	Lelio R Paula	10/2016
9043	(106*10^102422+17)/3	102424	Robert Price	04/2021
9044	24466^15349+15349^24466	102417	Hans Havermann	03/2019
9045	2^340212+111546435	102415	Paul Bourdelais	10/2021
9046	2^340208-20373	102413	Enzo Doria	06/2013
9047	6^131598-17273	102404	Enzo Doria	02/2013
9048	(2^340132+1182)/2	102390	Stefano Morozzi	09/2020
9049	(2^340133+1166)/2	102390	Stefano Morozzi	09/2020
9050	2^340115-21181	102385	Enzo Doria	06/2013
9051	(55459*2^340090+1)/1591	102379	Lelio R Paula	07/2014
9052	(2^340064+3630)/2	102370	Stefano Morozzi	09/2020
9053	9348*31^68638+13	102369	Eric Chen	04/2024
9054	89^52511-88^52511	102365	Robert Price	06/2015
9055	3^214539-112756	102362	Enzo Doria	07/2014
9056	Phi(562221,2)/53723397926257372614541581386770268796893300042857	102361	Anonymous	06/2025
9057	23159^23450-23450^23159	102353	Norbert Schneider	12/2019
9058	2^340000-19877	102351	Enzo Doria	06/2013
9060	2^339990-114845	102348	Enzo Doria	05/2015
9059	311^41058-41058^311	102348	Norman Luhn	09/2024
9061	(3^214516-2)/51383	102346	Lelio R Paula	12/2013
9062	20^78661-99	102341	Lelio R Paula	09/2016
9063	2^339951-19585	102336	Enzo Doria	05/2013
9064	(17*10^102335-167)/3	102336	Robert Price	05/2022
9065	(13*2^339943+1)/45	102333	Lelio R Paula	12/2013
9066	(236282#+121441)/(121441*25499429)	102332	Makoto Morimoto	08/2020
9067	5*10^102323-91	102324	Robert Price	03/2021
9069	2^339889+29327	102317	Yves Minet	06/2010
9068	(167*10^102315-17)/3	102317	Robert Price	03/2020
9070	26348^7641+7641^26348	102314	Hans Havermann	03/2019
9071	Phi(239414,10)/6333218543	102303	Makoto Kamada	08/2019
9072	2^339834-109493	102301	Enzo Doria	04/2014
9073	(16*10^102299-19)/3	102300	Robert Price	02/2019
9074	(11^98221-5^98221)/6	102286	Robert Price	01/2013
9075	3^214365+1820	102279	Lelio R Paula	10/2016
9076	31978^1579+1579^31978	102278	Hans Havermann	03/2019
9077	(89*10^102262-467)/9	102263	Robert Price	04/2022
9078	(11*2^339705-1)/183	102261	Lelio R Paula	03/2014
9079	2^339694-16995	102259	Lelio R Paula	09/2016
9080	(56*10^102255+691)/9	102256	Robert Price	05/2019
9081	122^49008+121	102249	Norbert Schneider	10/2018
9082	(2^339652+3178)/2	102246	Stefano Morozzi	09/2020
9083	7^120985-38	102245	Lelio R Paula	10/2016
9084	10^102244+122961	102245	Patrick De Geest	12/2016
9085	10^102244-27	102244	Lelio R Paula	09/2016
9086	7^120982-62	102242	Lelio R Paula	10/2016
9087	(2^339640+2670)/2	102242	Stefano Morozzi	09/2020
9088	4*6^131382-5	102236	Lelio R Paula	11/2014
9089	(2^339607+3290)/2	102232	Stefano Morozzi	02/2021
9090	2^339586-1091	102226	Yves Minet	11/2012
9091	11^98161-3072000	102225	Enzo Doria	12/2012
9092	9*7^120961-4	102225	Lelio R Paula	11/2014
9093	5*3^214250+2	102224	Serge Batalov	10/2010
9094	12^94713-59	102213	Lelio R Paula	10/2016
9095	12^94705+89	102204	Lelio R Paula	10/2016
9096	L(2*339475)%(2^339475)	102193	Henri Lifchitz	06/2025
9097	2^339407-177	102172	Lelio R Paula	08/2011
9098	4*10^102163-57	102164	Robert Price	10/2018
9099	2^339355+65	102157	Lelio R Paula	07/2011
9100	(28*10^102142-31)/3	102143	Robert Price	12/2019
9101	(2^339323+47)/880715	102141	Lelio R Paula	12/2013
9102	(2^339268+1758)/2	102130	Stefano Morozzi	09/2020
9103	U(610865)	102130	Serge Batalov	07/2024
9104	s(178551)	102122	Robert Price	05/2020
9105	(797*10^102112-23)/9	102114	Robert Price	01/2022
9106	(5*10^102107+7)/3	102108	Tyler Busby	02/2023
9107	(2^339175+2790)/2	102102	Stefano Morozzi	02/2021
9110	2^339168+21	102100	Lelio R Paula	07/2011
9109	2^339167-108807	102100	Enzo Doria	03/2014
9108	(2^339169+42)/2	102100	Stefano Morozzi	09/2020
9111	2^339156+163	102097	Lelio R Paula	08/2011
9112	(2^339149+746)/2	102094	Stefano Morozzi	09/2020
9113	(25*10^102076-67)/3	102077	Robert Price	06/2019
9114	2^339081-4543	102074	Yves Minet	03/2019
9115	(3435^28867-1)/3434	102069	Serge Batalov	06/2022
9116	2*10^102062+77	102063	Robert Price	08/2020
9117	24327^15668+15668^24327	102053	Hans Havermann	02/2019
9118	10^102052+66793	102053	Patrick De Geest	09/2022
9120	10^102052-7000001	102052	Robert Price	06/2021
9119	10^102052-618623	102052	Patrick De Geest	09/2022
9121	2^339000-175635	102050	Stefano Morozzi	12/2021
9122	2^339000-151667	102050	Stefano Morozzi	12/2021
9123	2^338999+79289	102049	Stefano Morozzi	01/2022
9124	2^338998-63897	102049	Stefano Morozzi	12/2022
9125	2^338997+99659	102049	Stefano Morozzi	02/2023
9126	2^338994+188757	102048	Stefano Morozzi	05/2022
9127	2^338995+70785	102048	Stefano Morozzi	11/2022
9128	2^338994-12183	102048	Stefano Morozzi	12/2022
9129	2^338992+181591	102047	Stefano Morozzi	01/2022
9130	2^338992+136171	102047	Stefano Morozzi	03/2022
9131	2^338991-109435	102047	Stefano Morozzi	04/2022
9132	2^338991+193611	102047	Stefano Morozzi	09/2022
9133	2^338988-134619	102046	Stefano Morozzi	04/2022
9134	2^338987-62557	102046	Stefano Morozzi	12/2022
9135	2^338986-60141	102045	Stefano Morozzi	06/2022
9136	2^338986+98209	102045	Stefano Morozzi	11/2022
9137	2^338981+106391	102044	Stefano Morozzi	01/2022
9138	2^338982+34069	102044	Stefano Morozzi	03/2022
9139	2^338982-58781	102044	Stefano Morozzi	04/2022
9140	2^338980+70833	102044	Stefano Morozzi	11/2022
9141	2^338982-92111	102044	Stefano Morozzi	02/2023
9142	2^338977+83007	102043	Stefano Morozzi	02/2022
9143	2^338979-83601	102043	Stefano Morozzi	04/2022
9144	2^338975+28355	102042	Stefano Morozzi	01/2022
9145	2^338973+134619	102042	Stefano Morozzi	03/2022
9146	2^338974+183777	102042	Stefano Morozzi	03/2022
9147	2^338975+69293	102042	Stefano Morozzi	09/2022
9155	25080^11711+11711^25080	102041	Hans Havermann	02/2019
9148	2^338972+152343	102041	Stefano Morozzi	12/2021
9149	2^338972-180623	102041	Stefano Morozzi	02/2022
9150	2^338972+84441	102041	Stefano Morozzi	03/2022
9151	2^338971+64875	102041	Stefano Morozzi	05/2022
9152	2^338971+44985	102041	Stefano Morozzi	11/2022
9153	2^338971+145065	102041	Stefano Morozzi	11/2022
9154	2^338972-16635	102041	Stefano Morozzi	01/2023
9156	2^338968+53461	102040	Stefano Morozzi	01/2022
9157	2^338969+160175	102040	Stefano Morozzi	03/2022
9158	2^338967+13409	102040	Stefano Morozzi	04/2022
9159	2^338969+67635	102040	Stefano Morozzi	09/2022
9160	2^338969-15913	102040	Stefano Morozzi	01/2023
9161	2^338963-127455	102039	Stefano Morozzi	12/2021
9162	2^338963+132195	102039	Stefano Morozzi	02/2022
9163	2^338966+137919	102039	Stefano Morozzi	04/2022
9164	2^338963-87529	102039	Stefano Morozzi	12/2022
9165	2^338963-116859	102039	Stefano Morozzi	02/2023
9172	(2^338982-7)/1754517	102038	Lelio R Paula	12/2013
9166	2^338960+53935	102038	Stefano Morozzi	01/2022
9167	2^338962+83157	102038	Stefano Morozzi	02/2022
9168	2^338961+12341	102038	Stefano Morozzi	04/2022
9169	2^338960+63933	102038	Stefano Morozzi	05/2022
9170	2^338960+170791	102038	Stefano Morozzi	11/2022
9171	2^338962+21679	102038	Stefano Morozzi	11/2022
9173	2^338959-30919	102037	Stefano Morozzi	02/2022
9174	2^338959+164769	102037	Stefano Morozzi	05/2022
9175	2^338958-43161	102037	Stefano Morozzi	02/2023
9176	2^338954-177003	102036	Stefano Morozzi	12/2021
9177	2^338954+154207	102036	Stefano Morozzi	01/2022
9178	2^338956+182493	102036	Stefano Morozzi	02/2022
9179	2^338954+162715	102036	Stefano Morozzi	04/2022
9180	2^338955-158241	102036	Stefano Morozzi	04/2022
9181	2^338956-33395	102036	Stefano Morozzi	04/2022
9182	2^338954+190915	102036	Stefano Morozzi	06/2022
9183	2^338955+41643	102036	Stefano Morozzi	09/2022
9184	2^338954+194427	102036	Stefano Morozzi	09/2022
9185	2^338956+117967	102036	Stefano Morozzi	09/2022
9186	2^338956+195495	102036	Stefano Morozzi	11/2022
9187	2^338954-186371	102036	Stefano Morozzi	12/2022
9188	2^338950+175077	102035	Stefano Morozzi	12/2021
9189	2^338951-51687	102035	Stefano Morozzi	12/2021
9190	2^338951+66123	102035	Stefano Morozzi	06/2022
9191	2^338950+19317	102035	Stefano Morozzi	09/2022
9192	2^338951-161479	102035	Stefano Morozzi	12/2022
9193	2^338950-66335	102035	Stefano Morozzi	01/2023
9194	2^338951-41611	102035	Stefano Morozzi	02/2023
9195	2^338952-142887	102035	Stefano Morozzi	02/2023
9196	2^338949+85449	102034	Stefano Morozzi	03/2022
9197	2^338949-184585	102034	Stefano Morozzi	04/2022
9198	2^338949-88555	102034	Stefano Morozzi	12/2022
9199	2^338948+49393	102034	Stefano Morozzi	02/2023
9200	2^338949-17601	102034	Stefano Morozzi	02/2023
9201	2^338943+127103	102033	Stefano Morozzi	12/2021
9202	2^338944-84003	102033	Stefano Morozzi	04/2022
9203	2^338945+138605	102033	Stefano Morozzi	05/2022
9204	2^338943+95133	102033	Stefano Morozzi	11/2022
9205	2^338943+147435	102033	Stefano Morozzi	11/2022
9206	2^338943-116067	102033	Stefano Morozzi	01/2023
9207	2^338940+78607	102032	Stefano Morozzi	01/2022
9208	2^338942-86687	102032	Stefano Morozzi	12/2022
9209	2^338939+151569	102031	Stefano Morozzi	12/2021
9210	2^338938+183975	102031	Stefano Morozzi	03/2022
9211	2^338937-33429	102031	Stefano Morozzi	04/2022
9212	2^338939-183259	102031	Stefano Morozzi	04/2022
9213	2^338937-139951	102031	Stefano Morozzi	01/2023
9214	2^338938-40151	102031	Stefano Morozzi	01/2023
9215	2^338938+74449	102031	Stefano Morozzi	02/2023
9216	2^338935+179999	102030	Stefano Morozzi	01/2022
9217	2^338936+84147	102030	Stefano Morozzi	03/2022
9218	2^338935+171261	102030	Stefano Morozzi	11/2022
9219	2^338936-41355	102030	Stefano Morozzi	01/2023
9220	2^338931+2349	102029	Stefano Morozzi	12/2021
9221	2^338933+79935	102029	Stefano Morozzi	01/2022
9222	2^338930+33819	102029	Stefano Morozzi	03/2022
9223	2^338931-31555	102029	Stefano Morozzi	03/2022
9224	2^338933+64169	102029	Stefano Morozzi	05/2022
9225	2^338932-184965	102029	Stefano Morozzi	06/2022
9226	2^338932+66943	102029	Stefano Morozzi	09/2022
9227	2^338932+92995	102029	Stefano Morozzi	09/2022
9228	2^338931+97001	102029	Stefano Morozzi	11/2022
9229	2^338932-165453	102029	Stefano Morozzi	01/2023
9230	2^338933-40899	102029	Stefano Morozzi	01/2023
9231	2^338928+2367	102028	Stefano Morozzi	12/2021
9232	2^338927+52779	102028	Stefano Morozzi	01/2022
9233	2^338927-79539	102028	Stefano Morozzi	02/2022
9234	2^338929+60819	102028	Stefano Morozzi	03/2022
9235	2^338928-156959	102028	Stefano Morozzi	03/2022
9236	2^338927-63919	102028	Stefano Morozzi	12/2022
9237	2^338925+106631	102027	Stefano Morozzi	01/2022
9238	2^338926+80235	102027	Stefano Morozzi	01/2022
9239	2^338926+41607	102027	Stefano Morozzi	09/2022
9240	2^338925+195435	102027	Stefano Morozzi	11/2022
9241	2^338924-92885	102027	Stefano Morozzi	02/2023
9242	2^338922-27291	102026	Stefano Morozzi	12/2021
9243	2^338919-103849	102025	Stefano Morozzi	01/2022
9244	2^338919+130221	102025	Stefano Morozzi	01/2022
9245	2^338918-91967	102025	Stefano Morozzi	02/2023
9246	2^338917+561057	102025	Boyan Hu	03/2024
9247	2^338914-79121	102024	Stefano Morozzi	02/2022
9248	2^338916+134047	102024	Stefano Morozzi	03/2022
9249	2^338914-11315	102024	Stefano Morozzi	12/2022
9250	2^338910+81027	102023	Stefano Morozzi	01/2022

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PRP Records

Probable Primes Top 10000

(301815 PRPs in the top)